/**
* This file is part of ORB-SLAM.
*
* Copyright (C) 2014 Raúl Mur-Artal <raulmur at unizar dot es> (University of Zaragoza)
* For more information see <http://webdiis.unizar.es/~raulmur/orbslam/>
*
* ORB-SLAM is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* ORB-SLAM is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with ORB-SLAM. If not, see <http://www.gnu.org/licenses/>.
*/


#include <iostream>

#include "PnPsolver.hpp"

#include <vector>
#include <cmath>
#include <opencv2/opencv.hpp>
#include "Thirdparty/DBoW2/DUtils/Random.h"
#include <algorithm>

using namespace std;

namespace ORB_SLAM
{
    
    
    PnPsolver::PnPsolver(const Frame &F, const vector<MapPoint*> &vpMapPointMatches):
    pws(0), us(0), alphas(0), pcs(0), maximum_number_of_correspondences(0), number_of_correspondences(0), mnInliersi(0),
    mnIterations(0), mnBestInliers(0), N(0)
    {
        mvpMapPointMatches = vpMapPointMatches;
        mvP2D.reserve(F.mvpMapPoints.size());
        mvSigma2.reserve(F.mvpMapPoints.size());
        mvP3Dw.reserve(F.mvpMapPoints.size());
        mvKeyPointIndices.reserve(F.mvpMapPoints.size());
        mvAllIndices.reserve(F.mvpMapPoints.size());
        
        int idx=0;
        for(size_t i=0, iend=vpMapPointMatches.size(); i<iend; i++)
        {
            MapPoint* pMP = vpMapPointMatches[i];
            
            if(pMP)
            {
                if(!pMP->isBad())
                {
                    const cv::KeyPoint &kp = F.mvKeysUn[i];
                    
                    mvP2D.push_back(kp.pt);
                    mvSigma2.push_back(F.mvLevelSigma2[kp.octave]);
                    
                    cv::Mat Pos = pMP->GetWorldPos();
                    mvP3Dw.push_back(cv::Point3f(Pos.at<float>(0),Pos.at<float>(1), Pos.at<float>(2)));
                    
                    mvKeyPointIndices.push_back(i);
                    mvAllIndices.push_back(idx);
                    
                    idx++;
                }
            }
        }
        
        // Set camera calibration parameters
        fu = F.fx;
        fv = F.fy;
        uc = F.cx;
        vc = F.cy;
        
        SetRansacParameters();
    }
    
    PnPsolver::~PnPsolver()
    {
        delete [] pws;
        delete [] us;
        delete [] alphas;
        delete [] pcs;
    }
    
    
    void PnPsolver::SetRansacParameters(double probability, int minInliers, int maxIterations, int minSet, float epsilon, float th2)
    {
        mRansacProb = probability;
        mRansacMinInliers = minInliers;
        mRansacMaxIts = maxIterations;
        mRansacEpsilon = epsilon;
        mRansacMinSet = minSet;
        
        N = mvP2D.size(); // number of correspondences
        
        mvbInliersi.resize(N);
        
        // Adjust Parameters according to number of correspondences
        int nMinInliers = N*mRansacEpsilon;
        if(nMinInliers<mRansacMinInliers)
            nMinInliers=mRansacMinInliers;
        if(nMinInliers<minSet)
            nMinInliers=minSet;
        mRansacMinInliers = nMinInliers;
        
        if(mRansacEpsilon<(float)mRansacMinInliers/N)
            mRansacEpsilon=(float)mRansacMinInliers/N;
        
        // Set RANSAC iterations according to probability, epsilon, and max iterations
        int nIterations;
        
        if(mRansacMinInliers==N)
            nIterations=1;
        else
            nIterations = ceil(log(1-mRansacProb)/log(1-pow(mRansacEpsilon,3)));
        
        mRansacMaxIts = max(1,min(nIterations,mRansacMaxIts));
        
        mvMaxError.resize(mvSigma2.size());
        for(size_t i=0; i<mvSigma2.size(); i++)
            mvMaxError[i] = mvSigma2[i]*th2;
    }
    
    cv::Mat PnPsolver::find(vector<bool> &vbInliers, int &nInliers)
    {
        bool bFlag;
        return iterate(mRansacMaxIts,bFlag,vbInliers,nInliers);
    }
    
    cv::Mat PnPsolver::iterate(int nIterations, bool &bNoMore, vector<bool> &vbInliers, int &nInliers)
    {
        bNoMore = false;
        vbInliers.clear();
        nInliers=0;
        
        set_maximum_number_of_correspondences(mRansacMinSet);
        
        if(N<mRansacMinInliers)
        {
            bNoMore = true;
            return cv::Mat();
        }
        
        vector<size_t> vAvailableIndices;
        
        int nCurrentIterations = 0;
        while(mnIterations<mRansacMaxIts || nCurrentIterations<nIterations)
        {
            nCurrentIterations++;
            mnIterations++;
            reset_correspondences();
            
            vAvailableIndices = mvAllIndices;
            
            // Get min set of points
            for(short i = 0; i < mRansacMinSet; ++i)
            {
                int randi = DUtils::Random::RandomInt(0, vAvailableIndices.size()-1);
                
                int idx = vAvailableIndices[randi];
                
                add_correspondence(mvP3Dw[idx].x,mvP3Dw[idx].y,mvP3Dw[idx].z,mvP2D[idx].x,mvP2D[idx].y);
                
                vAvailableIndices[idx] = vAvailableIndices.back();
                vAvailableIndices.pop_back();
            }
            
            // Compute camera pose
            compute_pose(mRi, mti);
            
            // Check inliers
            CheckInliers();
            
            if(mnInliersi>=mRansacMinInliers)
            {
                // If it is the best solution so far, save it
                if(mnInliersi>mnBestInliers)
                {
                    mvbBestInliers = mvbInliersi;
                    mnBestInliers = mnInliersi;
                    
                    cv::Mat Rcw(3,3,CV_64F,mRi);
                    cv::Mat tcw(3,1,CV_64F,mti);
                    Rcw.convertTo(Rcw,CV_32F);
                    tcw.convertTo(tcw,CV_32F);
                    mBestTcw = cv::Mat::eye(4,4,CV_32F);
                    Rcw.copyTo(mBestTcw.rowRange(0,3).colRange(0,3));
                    tcw.copyTo(mBestTcw.rowRange(0,3).col(3));
                }
                
                if(Refine())
                {
                    nInliers = mnRefinedInliers;
                    vbInliers = vector<bool>(mvpMapPointMatches.size(),false);
                    for(int i=0; i<N; i++)
                    {
                        if(mvbRefinedInliers[i])
                            vbInliers[mvKeyPointIndices[i]] = true;
                    }
                    return mRefinedTcw.clone();
                }
                
            }
        }
        
        if(mnIterations>=mRansacMaxIts)
        {
            bNoMore=true;
            if(mnBestInliers>=mRansacMinInliers)
            {
                nInliers=mnBestInliers;
                vbInliers = vector<bool>(mvpMapPointMatches.size(),false);
                for(int i=0; i<N; i++)
                {
                    if(mvbBestInliers[i])
                        vbInliers[mvKeyPointIndices[i]] = true;
                }
                return mBestTcw.clone();
            }
        }
        
        return cv::Mat();
    }
    
    bool PnPsolver::Refine()
    {
        vector<int> vIndices;
        vIndices.reserve(mvbBestInliers.size());
        
        for(size_t i=0; i<mvbBestInliers.size(); i++)
        {
            if(mvbBestInliers[i])
            {
                vIndices.push_back(i);
            }
        }
        
        set_maximum_number_of_correspondences(vIndices.size());
        
        reset_correspondences();
        
        for(size_t i=0; i<vIndices.size(); i++)
        {
            int idx = vIndices[i];
            add_correspondence(mvP3Dw[idx].x,mvP3Dw[idx].y,mvP3Dw[idx].z,mvP2D[idx].x,mvP2D[idx].y);
        }
        
        // Compute camera pose
        compute_pose(mRi, mti);
        
        // Check inliers
        CheckInliers();
        
        mnRefinedInliers =mnInliersi;
        mvbRefinedInliers = mvbInliersi;
        
        if(mnInliersi>mRansacMinInliers)
        {
            cv::Mat Rcw(3,3,CV_64F,mRi);
            cv::Mat tcw(3,1,CV_64F,mti);
            Rcw.convertTo(Rcw,CV_32F);
            tcw.convertTo(tcw,CV_32F);
            mRefinedTcw = cv::Mat::eye(4,4,CV_32F);
            Rcw.copyTo(mRefinedTcw.rowRange(0,3).colRange(0,3));
            tcw.copyTo(mRefinedTcw.rowRange(0,3).col(3));
            return true;
        }
        
        return false;
    }
    
    
    void PnPsolver::CheckInliers()
    {
        mnInliersi=0;
        
        for(int i=0; i<N; i++)
        {
            cv::Point3f P3Dw = mvP3Dw[i];
            cv::Point2f P2D = mvP2D[i];
            
            float Xc = mRi[0][0]*P3Dw.x+mRi[0][1]*P3Dw.y+mRi[0][2]*P3Dw.z+mti[0];
            float Yc = mRi[1][0]*P3Dw.x+mRi[1][1]*P3Dw.y+mRi[1][2]*P3Dw.z+mti[1];
            float invZc = 1/(mRi[2][0]*P3Dw.x+mRi[2][1]*P3Dw.y+mRi[2][2]*P3Dw.z+mti[2]);
            
            double ue = uc + fu * Xc * invZc;
            double ve = vc + fv * Yc * invZc;
            
            float distX = P2D.x-ue;
            float distY = P2D.y-ve;
            
            float error2 = distX*distX+distY*distY;
            
            if(error2<mvMaxError[i])
            {
                mvbInliersi[i]=true;
                mnInliersi++;
            }
            else
            {
                mvbInliersi[i]=false;
            }
        }
    }
    
    
    void PnPsolver::set_maximum_number_of_correspondences(int n)
    {
        if (maximum_number_of_correspondences < n) {
            if (pws != 0) delete [] pws;
            if (us != 0) delete [] us;
            if (alphas != 0) delete [] alphas;
            if (pcs != 0) delete [] pcs;
            
            maximum_number_of_correspondences = n;
            pws = new double[3 * maximum_number_of_correspondences];
            us = new double[2 * maximum_number_of_correspondences];
            alphas = new double[4 * maximum_number_of_correspondences];
            pcs = new double[3 * maximum_number_of_correspondences];
        }
    }
    
    void PnPsolver::reset_correspondences(void)
    {
        number_of_correspondences = 0;
    }
    
    void PnPsolver::add_correspondence(double X, double Y, double Z, double u, double v)
    {
        pws[3 * number_of_correspondences    ] = X;
        pws[3 * number_of_correspondences + 1] = Y;
        pws[3 * number_of_correspondences + 2] = Z;
        
        us[2 * number_of_correspondences    ] = u;
        us[2 * number_of_correspondences + 1] = v;
        
        number_of_correspondences++;
    }
    
    void PnPsolver::choose_control_points(void)
    {
        // Take C0 as the reference points centroid:
        cws[0][0] = cws[0][1] = cws[0][2] = 0;
        for(int i = 0; i < number_of_correspondences; i++)
            for(int j = 0; j < 3; j++)
                cws[0][j] += pws[3 * i + j];
        
        for(int j = 0; j < 3; j++)
            cws[0][j] /= number_of_correspondences;
        
        
        // Take C1, C2, and C3 from PCA on the reference points:
        CvMat * PW0 = cvCreateMat(number_of_correspondences, 3, CV_64F);
        
        double pw0tpw0[3 * 3], dc[3], uct[3 * 3];
        CvMat PW0tPW0 = cvMat(3, 3, CV_64F, pw0tpw0);
        CvMat DC      = cvMat(3, 1, CV_64F, dc);
        CvMat UCt     = cvMat(3, 3, CV_64F, uct);
        
        for(int i = 0; i < number_of_correspondences; i++)
            for(int j = 0; j < 3; j++)
                PW0->data.db[3 * i + j] = pws[3 * i + j] - cws[0][j];
        
        cvMulTransposed(PW0, &PW0tPW0, 1);
        cvSVD(&PW0tPW0, &DC, &UCt, 0, CV_SVD_MODIFY_A | CV_SVD_U_T);
        
        cvReleaseMat(&PW0);
        
        for(int i = 1; i < 4; i++) {
            double k = sqrt(dc[i - 1] / number_of_correspondences);
            for(int j = 0; j < 3; j++)
                cws[i][j] = cws[0][j] + k * uct[3 * (i - 1) + j];
        }
    }
    
    void PnPsolver::compute_barycentric_coordinates(void)
    {
        double cc[3 * 3], cc_inv[3 * 3];
        CvMat CC     = cvMat(3, 3, CV_64F, cc);
        CvMat CC_inv = cvMat(3, 3, CV_64F, cc_inv);
        
        for(int i = 0; i < 3; i++)
            for(int j = 1; j < 4; j++)
                cc[3 * i + j - 1] = cws[j][i] - cws[0][i];
        
        cvInvert(&CC, &CC_inv, CV_SVD);
        double * ci = cc_inv;
        for(int i = 0; i < number_of_correspondences; i++) {
            double * pi = pws + 3 * i;
            double * a = alphas + 4 * i;
            
            for(int j = 0; j < 3; j++)
                a[1 + j] =
                ci[3 * j    ] * (pi[0] - cws[0][0]) +
                ci[3 * j + 1] * (pi[1] - cws[0][1]) +
                ci[3 * j + 2] * (pi[2] - cws[0][2]);
            a[0] = 1.0f - a[1] - a[2] - a[3];
        }
    }
    
    void PnPsolver::fill_M(CvMat * M,
                           const int row, const double * as, const double u, const double v)
    {
        double * M1 = M->data.db + row * 12;
        double * M2 = M1 + 12;
        
        for(int i = 0; i < 4; i++) {
            M1[3 * i    ] = as[i] * fu;
            M1[3 * i + 1] = 0.0;
            M1[3 * i + 2] = as[i] * (uc - u);
            
            M2[3 * i    ] = 0.0;
            M2[3 * i + 1] = as[i] * fv;
            M2[3 * i + 2] = as[i] * (vc - v);
        }
    }
    
    void PnPsolver::compute_ccs(const double * betas, const double * ut)
    {
        for(int i = 0; i < 4; i++)
            ccs[i][0] = ccs[i][1] = ccs[i][2] = 0.0f;
        
        for(int i = 0; i < 4; i++) {
            const double * v = ut + 12 * (11 - i);
            for(int j = 0; j < 4; j++)
                for(int k = 0; k < 3; k++)
                    ccs[j][k] += betas[i] * v[3 * j + k];
        }
    }
    
    void PnPsolver::compute_pcs(void)
    {
        for(int i = 0; i < number_of_correspondences; i++) {
            double * a = alphas + 4 * i;
            double * pc = pcs + 3 * i;
            
            for(int j = 0; j < 3; j++)
                pc[j] = a[0] * ccs[0][j] + a[1] * ccs[1][j] + a[2] * ccs[2][j] + a[3] * ccs[3][j];
        }
    }
    
    double PnPsolver::compute_pose(double R[3][3], double t[3])
    {
        choose_control_points();
        compute_barycentric_coordinates();
        
        CvMat * M = cvCreateMat(2 * number_of_correspondences, 12, CV_64F);
        
        for(int i = 0; i < number_of_correspondences; i++)
            fill_M(M, 2 * i, alphas + 4 * i, us[2 * i], us[2 * i + 1]);
        
        double mtm[12 * 12], d[12], ut[12 * 12];
        CvMat MtM = cvMat(12, 12, CV_64F, mtm);
        CvMat D   = cvMat(12,  1, CV_64F, d);
        CvMat Ut  = cvMat(12, 12, CV_64F, ut);
        
        cvMulTransposed(M, &MtM, 1);
        cvSVD(&MtM, &D, &Ut, 0, CV_SVD_MODIFY_A | CV_SVD_U_T);
        cvReleaseMat(&M);
        
        double l_6x10[6 * 10], rho[6];
        CvMat L_6x10 = cvMat(6, 10, CV_64F, l_6x10);
        CvMat Rho    = cvMat(6,  1, CV_64F, rho);
        
        compute_L_6x10(ut, l_6x10);
        compute_rho(rho);
        
        double Betas[4][4], rep_errors[4];
        double Rs[4][3][3], ts[4][3];
        
        find_betas_approx_1(&L_6x10, &Rho, Betas[1]);
        gauss_newton(&L_6x10, &Rho, Betas[1]);
        rep_errors[1] = compute_R_and_t(ut, Betas[1], Rs[1], ts[1]);
        
        find_betas_approx_2(&L_6x10, &Rho, Betas[2]);
        gauss_newton(&L_6x10, &Rho, Betas[2]);
        rep_errors[2] = compute_R_and_t(ut, Betas[2], Rs[2], ts[2]);
        
        find_betas_approx_3(&L_6x10, &Rho, Betas[3]);
        gauss_newton(&L_6x10, &Rho, Betas[3]);
        rep_errors[3] = compute_R_and_t(ut, Betas[3], Rs[3], ts[3]);
        
        int N = 1;
        if (rep_errors[2] < rep_errors[1]) N = 2;
        if (rep_errors[3] < rep_errors[N]) N = 3;
        
        copy_R_and_t(Rs[N], ts[N], R, t);
        
        return rep_errors[N];
    }
    
    void PnPsolver::copy_R_and_t(const double R_src[3][3], const double t_src[3],
                                 double R_dst[3][3], double t_dst[3])
    {
        for(int i = 0; i < 3; i++) {
            for(int j = 0; j < 3; j++)
                R_dst[i][j] = R_src[i][j];
            t_dst[i] = t_src[i];
        }
    }
    
    double PnPsolver::dist2(const double * p1, const double * p2)
    {
        return
        (p1[0] - p2[0]) * (p1[0] - p2[0]) +
        (p1[1] - p2[1]) * (p1[1] - p2[1]) +
        (p1[2] - p2[2]) * (p1[2] - p2[2]);
    }
    
    double PnPsolver::dot(const double * v1, const double * v2)
    {
        return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
    }
    
    double PnPsolver::reprojection_error(const double R[3][3], const double t[3])
    {
        double sum2 = 0.0;
        
        for(int i = 0; i < number_of_correspondences; i++) {
            double * pw = pws + 3 * i;
            double Xc = dot(R[0], pw) + t[0];
            double Yc = dot(R[1], pw) + t[1];
            double inv_Zc = 1.0 / (dot(R[2], pw) + t[2]);
            double ue = uc + fu * Xc * inv_Zc;
            double ve = vc + fv * Yc * inv_Zc;
            double u = us[2 * i], v = us[2 * i + 1];
            
            sum2 += sqrt( (u - ue) * (u - ue) + (v - ve) * (v - ve) );
        }
        
        return sum2 / number_of_correspondences;
    }
    
    void PnPsolver::estimate_R_and_t(double R[3][3], double t[3])
    {
        double pc0[3], pw0[3];
        
        pc0[0] = pc0[1] = pc0[2] = 0.0;
        pw0[0] = pw0[1] = pw0[2] = 0.0;
        
        for(int i = 0; i < number_of_correspondences; i++) {
            const double * pc = pcs + 3 * i;
            const double * pw = pws + 3 * i;
            
            for(int j = 0; j < 3; j++) {
                pc0[j] += pc[j];
                pw0[j] += pw[j];
            }
        }
        for(int j = 0; j < 3; j++) {
            pc0[j] /= number_of_correspondences;
            pw0[j] /= number_of_correspondences;
        }
        
        double abt[3 * 3], abt_d[3], abt_u[3 * 3], abt_v[3 * 3];
        CvMat ABt   = cvMat(3, 3, CV_64F, abt);
        CvMat ABt_D = cvMat(3, 1, CV_64F, abt_d);
        CvMat ABt_U = cvMat(3, 3, CV_64F, abt_u);
        CvMat ABt_V = cvMat(3, 3, CV_64F, abt_v);
        
        cvSetZero(&ABt);
        for(int i = 0; i < number_of_correspondences; i++) {
            double * pc = pcs + 3 * i;
            double * pw = pws + 3 * i;
            
            for(int j = 0; j < 3; j++) {
                abt[3 * j    ] += (pc[j] - pc0[j]) * (pw[0] - pw0[0]);
                abt[3 * j + 1] += (pc[j] - pc0[j]) * (pw[1] - pw0[1]);
                abt[3 * j + 2] += (pc[j] - pc0[j]) * (pw[2] - pw0[2]);
            }
        }
        
        cvSVD(&ABt, &ABt_D, &ABt_U, &ABt_V, CV_SVD_MODIFY_A);
        
        for(int i = 0; i < 3; i++)
            for(int j = 0; j < 3; j++)
                R[i][j] = dot(abt_u + 3 * i, abt_v + 3 * j);
        
        const double det =
        R[0][0] * R[1][1] * R[2][2] + R[0][1] * R[1][2] * R[2][0] + R[0][2] * R[1][0] * R[2][1] -
        R[0][2] * R[1][1] * R[2][0] - R[0][1] * R[1][0] * R[2][2] - R[0][0] * R[1][2] * R[2][1];
        
        if (det < 0) {
            R[2][0] = -R[2][0];
            R[2][1] = -R[2][1];
            R[2][2] = -R[2][2];
        }
        
        t[0] = pc0[0] - dot(R[0], pw0);
        t[1] = pc0[1] - dot(R[1], pw0);
        t[2] = pc0[2] - dot(R[2], pw0);
    }
    
    void PnPsolver::print_pose(const double R[3][3], const double t[3])
    {
        cout << R[0][0] << " " << R[0][1] << " " << R[0][2] << " " << t[0] << endl;
        cout << R[1][0] << " " << R[1][1] << " " << R[1][2] << " " << t[1] << endl;
        cout << R[2][0] << " " << R[2][1] << " " << R[2][2] << " " << t[2] << endl;
    }
    
    void PnPsolver::solve_for_sign(void)
    {
        if (pcs[2] < 0.0) {
            for(int i = 0; i < 4; i++)
                for(int j = 0; j < 3; j++)
                    ccs[i][j] = -ccs[i][j];
            
            for(int i = 0; i < number_of_correspondences; i++) {
                pcs[3 * i    ] = -pcs[3 * i];
                pcs[3 * i + 1] = -pcs[3 * i + 1];
                pcs[3 * i + 2] = -pcs[3 * i + 2];
            }
        }
    }
    
    double PnPsolver::compute_R_and_t(const double * ut, const double * betas,
                                      double R[3][3], double t[3])
    {
        compute_ccs(betas, ut);
        compute_pcs();
        
        solve_for_sign();
        
        estimate_R_and_t(R, t);
        
        return reprojection_error(R, t);
    }
    
    // betas10        = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44]
    // betas_approx_1 = [B11 B12     B13         B14]
    
    void PnPsolver::find_betas_approx_1(const CvMat * L_6x10, const CvMat * Rho,
                                        double * betas)
    {
        double l_6x4[6 * 4], b4[4];
        CvMat L_6x4 = cvMat(6, 4, CV_64F, l_6x4);
        CvMat B4    = cvMat(4, 1, CV_64F, b4);
        
        for(int i = 0; i < 6; i++) {
            cvmSet(&L_6x4, i, 0, cvmGet(L_6x10, i, 0));
            cvmSet(&L_6x4, i, 1, cvmGet(L_6x10, i, 1));
            cvmSet(&L_6x4, i, 2, cvmGet(L_6x10, i, 3));
            cvmSet(&L_6x4, i, 3, cvmGet(L_6x10, i, 6));
        }
        
        cvSolve(&L_6x4, Rho, &B4, CV_SVD);
        
        if (b4[0] < 0) {
            betas[0] = sqrt(-b4[0]);
            betas[1] = -b4[1] / betas[0];
            betas[2] = -b4[2] / betas[0];
            betas[3] = -b4[3] / betas[0];
        } else {
            betas[0] = sqrt(b4[0]);
            betas[1] = b4[1] / betas[0];
            betas[2] = b4[2] / betas[0];
            betas[3] = b4[3] / betas[0];
        }
    }
    
    // betas10        = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44]
    // betas_approx_2 = [B11 B12 B22                            ]
    
    void PnPsolver::find_betas_approx_2(const CvMat * L_6x10, const CvMat * Rho,
                                        double * betas)
    {
        double l_6x3[6 * 3], b3[3];
        CvMat L_6x3  = cvMat(6, 3, CV_64F, l_6x3);
        CvMat B3     = cvMat(3, 1, CV_64F, b3);
        
        for(int i = 0; i < 6; i++) {
            cvmSet(&L_6x3, i, 0, cvmGet(L_6x10, i, 0));
            cvmSet(&L_6x3, i, 1, cvmGet(L_6x10, i, 1));
            cvmSet(&L_6x3, i, 2, cvmGet(L_6x10, i, 2));
        }
        
        cvSolve(&L_6x3, Rho, &B3, CV_SVD);
        
        if (b3[0] < 0) {
            betas[0] = sqrt(-b3[0]);
            betas[1] = (b3[2] < 0) ? sqrt(-b3[2]) : 0.0;
        } else {
            betas[0] = sqrt(b3[0]);
            betas[1] = (b3[2] > 0) ? sqrt(b3[2]) : 0.0;
        }
        
        if (b3[1] < 0) betas[0] = -betas[0];
        
        betas[2] = 0.0;
        betas[3] = 0.0;
    }
    
    // betas10        = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44]
    // betas_approx_3 = [B11 B12 B22 B13 B23                    ]
    
    void PnPsolver::find_betas_approx_3(const CvMat * L_6x10, const CvMat * Rho,
                                        double * betas)
    {
        double l_6x5[6 * 5], b5[5];
        CvMat L_6x5 = cvMat(6, 5, CV_64F, l_6x5);
        CvMat B5    = cvMat(5, 1, CV_64F, b5);
        
        for(int i = 0; i < 6; i++) {
            cvmSet(&L_6x5, i, 0, cvmGet(L_6x10, i, 0));
            cvmSet(&L_6x5, i, 1, cvmGet(L_6x10, i, 1));
            cvmSet(&L_6x5, i, 2, cvmGet(L_6x10, i, 2));
            cvmSet(&L_6x5, i, 3, cvmGet(L_6x10, i, 3));
            cvmSet(&L_6x5, i, 4, cvmGet(L_6x10, i, 4));
        }
        
        cvSolve(&L_6x5, Rho, &B5, CV_SVD);
        
        if (b5[0] < 0) {
            betas[0] = sqrt(-b5[0]);
            betas[1] = (b5[2] < 0) ? sqrt(-b5[2]) : 0.0;
        } else {
            betas[0] = sqrt(b5[0]);
            betas[1] = (b5[2] > 0) ? sqrt(b5[2]) : 0.0;
        }
        if (b5[1] < 0) betas[0] = -betas[0];
        betas[2] = b5[3] / betas[0];
        betas[3] = 0.0;
    }
    
    void PnPsolver::compute_L_6x10(const double * ut, double * l_6x10)
    {
        const double * v[4];
        
        v[0] = ut + 12 * 11;
        v[1] = ut + 12 * 10;
        v[2] = ut + 12 *  9;
        v[3] = ut + 12 *  8;
        
        double dv[4][6][3];
        
        for(int i = 0; i < 4; i++) {
            int a = 0, b = 1;
            for(int j = 0; j < 6; j++) {
                dv[i][j][0] = v[i][3 * a    ] - v[i][3 * b];
                dv[i][j][1] = v[i][3 * a + 1] - v[i][3 * b + 1];
                dv[i][j][2] = v[i][3 * a + 2] - v[i][3 * b + 2];
                
                b++;
                if (b > 3) {
                    a++;
                    b = a + 1;
                }
            }
        }
        
        for(int i = 0; i < 6; i++) {
            double * row = l_6x10 + 10 * i;
            
            row[0] =        dot(dv[0][i], dv[0][i]);
            row[1] = 2.0f * dot(dv[0][i], dv[1][i]);
            row[2] =        dot(dv[1][i], dv[1][i]);
            row[3] = 2.0f * dot(dv[0][i], dv[2][i]);
            row[4] = 2.0f * dot(dv[1][i], dv[2][i]);
            row[5] =        dot(dv[2][i], dv[2][i]);
            row[6] = 2.0f * dot(dv[0][i], dv[3][i]);
            row[7] = 2.0f * dot(dv[1][i], dv[3][i]);
            row[8] = 2.0f * dot(dv[2][i], dv[3][i]);
            row[9] =        dot(dv[3][i], dv[3][i]);
        }
    }
    
    void PnPsolver::compute_rho(double * rho)
    {
        rho[0] = dist2(cws[0], cws[1]);
        rho[1] = dist2(cws[0], cws[2]);
        rho[2] = dist2(cws[0], cws[3]);
        rho[3] = dist2(cws[1], cws[2]);
        rho[4] = dist2(cws[1], cws[3]);
        rho[5] = dist2(cws[2], cws[3]);
    }
    
    void PnPsolver::compute_A_and_b_gauss_newton(const double * l_6x10, const double * rho,
                                                 double betas[4], CvMat * A, CvMat * b)
    {
        for(int i = 0; i < 6; i++) {
            const double * rowL = l_6x10 + i * 10;
            double * rowA = A->data.db + i * 4;
            
            rowA[0] = 2 * rowL[0] * betas[0] +     rowL[1] * betas[1] +     rowL[3] * betas[2] +     rowL[6] * betas[3];
            rowA[1] =     rowL[1] * betas[0] + 2 * rowL[2] * betas[1] +     rowL[4] * betas[2] +     rowL[7] * betas[3];
            rowA[2] =     rowL[3] * betas[0] +     rowL[4] * betas[1] + 2 * rowL[5] * betas[2] +     rowL[8] * betas[3];
            rowA[3] =     rowL[6] * betas[0] +     rowL[7] * betas[1] +     rowL[8] * betas[2] + 2 * rowL[9] * betas[3];
            
            cvmSet(b, i, 0, rho[i] -
                   (
                    rowL[0] * betas[0] * betas[0] +
                    rowL[1] * betas[0] * betas[1] +
                    rowL[2] * betas[1] * betas[1] +
                    rowL[3] * betas[0] * betas[2] +
                    rowL[4] * betas[1] * betas[2] +
                    rowL[5] * betas[2] * betas[2] +
                    rowL[6] * betas[0] * betas[3] +
                    rowL[7] * betas[1] * betas[3] +
                    rowL[8] * betas[2] * betas[3] +
                    rowL[9] * betas[3] * betas[3]
                    ));
        }
    }
    
    void PnPsolver::gauss_newton(const CvMat * L_6x10, const CvMat * Rho,
                                 double betas[4])
    {
        const int iterations_number = 5;
        
        double a[6*4], b[6], x[4];
        CvMat A = cvMat(6, 4, CV_64F, a);
        CvMat B = cvMat(6, 1, CV_64F, b);
        CvMat X = cvMat(4, 1, CV_64F, x);
        
        for(int k = 0; k < iterations_number; k++) {
            compute_A_and_b_gauss_newton(L_6x10->data.db, Rho->data.db,
                                         betas, &A, &B);
            qr_solve(&A, &B, &X);
            
            for(int i = 0; i < 4; i++)
                betas[i] += x[i];
        }
    }
    
    void PnPsolver::qr_solve(CvMat * A, CvMat * b, CvMat * X)
    {
        static int max_nr = 0;
        static double * A1, * A2;
        
        const int nr = A->rows;
        const int nc = A->cols;
        
        if (max_nr != 0 && max_nr < nr) {
            delete [] A1;
            delete [] A2;
        }
        if (max_nr < nr) {
            max_nr = nr;
            A1 = new double[nr];
            A2 = new double[nr];
        }
        
        double * pA = A->data.db, * ppAkk = pA;
        for(int k = 0; k < nc; k++) {
            double * ppAik = ppAkk, eta = fabs(*ppAik);
            for(int i = k + 1; i < nr; i++) {
                double elt = fabs(*ppAik);
                if (eta < elt) eta = elt;
                ppAik += nc;
            }
            
            if (eta == 0) {
                A1[k] = A2[k] = 0.0;
                cerr << "God damnit, A is singular, this shouldn't happen." << endl;
                return;
            } else {
                double * ppAik = ppAkk, sum = 0.0, inv_eta = 1. / eta;
                for(int i = k; i < nr; i++) {
                    *ppAik *= inv_eta;
                    sum += *ppAik * *ppAik;
                    ppAik += nc;
                }
                double sigma = sqrt(sum);
                if (*ppAkk < 0)
                    sigma = -sigma;
                *ppAkk += sigma;
                A1[k] = sigma * *ppAkk;
                A2[k] = -eta * sigma;
                for(int j = k + 1; j < nc; j++) {
                    double * ppAik = ppAkk, sum = 0;
                    for(int i = k; i < nr; i++) {
                        sum += *ppAik * ppAik[j - k];
                        ppAik += nc;
                    }
                    double tau = sum / A1[k];
                    ppAik = ppAkk;
                    for(int i = k; i < nr; i++) {
                        ppAik[j - k] -= tau * *ppAik;
                        ppAik += nc;
                    }
                }
            }
            ppAkk += nc + 1;
        }
        
        // b <- Qt b
        double * ppAjj = pA, * pb = b->data.db;
        for(int j = 0; j < nc; j++) {
            double * ppAij = ppAjj, tau = 0;
            for(int i = j; i < nr; i++)	{
                tau += *ppAij * pb[i];
                ppAij += nc;
            }
            tau /= A1[j];
            ppAij = ppAjj;
            for(int i = j; i < nr; i++) {
                pb[i] -= tau * *ppAij;
                ppAij += nc;
            }
            ppAjj += nc + 1;
        }
        
        // X = R-1 b
        double * pX = X->data.db;
        pX[nc - 1] = pb[nc - 1] / A2[nc - 1];
        for(int i = nc - 2; i >= 0; i--) {
            double * ppAij = pA + i * nc + (i + 1), sum = 0;
            
            for(int j = i + 1; j < nc; j++) {
                sum += *ppAij * pX[j];
                ppAij++;
            }
            pX[i] = (pb[i] - sum) / A2[i];
        }
    }
    
    
    
    void PnPsolver::relative_error(double & rot_err, double & transl_err,
                                   const double Rtrue[3][3], const double ttrue[3],
                                   const double Rest[3][3],  const double test[3])
    {
        double qtrue[4], qest[4];
        
        mat_to_quat(Rtrue, qtrue);
        mat_to_quat(Rest, qest);
        
        double rot_err1 = sqrt((qtrue[0] - qest[0]) * (qtrue[0] - qest[0]) +
                               (qtrue[1] - qest[1]) * (qtrue[1] - qest[1]) +
                               (qtrue[2] - qest[2]) * (qtrue[2] - qest[2]) +
                               (qtrue[3] - qest[3]) * (qtrue[3] - qest[3]) ) /
        sqrt(qtrue[0] * qtrue[0] + qtrue[1] * qtrue[1] + qtrue[2] * qtrue[2] + qtrue[3] * qtrue[3]);
        
        double rot_err2 = sqrt((qtrue[0] + qest[0]) * (qtrue[0] + qest[0]) +
                               (qtrue[1] + qest[1]) * (qtrue[1] + qest[1]) +
                               (qtrue[2] + qest[2]) * (qtrue[2] + qest[2]) +
                               (qtrue[3] + qest[3]) * (qtrue[3] + qest[3]) ) /
        sqrt(qtrue[0] * qtrue[0] + qtrue[1] * qtrue[1] + qtrue[2] * qtrue[2] + qtrue[3] * qtrue[3]);
        
        rot_err = min(rot_err1, rot_err2);
        
        transl_err =
        sqrt((ttrue[0] - test[0]) * (ttrue[0] - test[0]) +
             (ttrue[1] - test[1]) * (ttrue[1] - test[1]) +
             (ttrue[2] - test[2]) * (ttrue[2] - test[2])) /
        sqrt(ttrue[0] * ttrue[0] + ttrue[1] * ttrue[1] + ttrue[2] * ttrue[2]);
    }
    
    void PnPsolver::mat_to_quat(const double R[3][3], double q[4])
    {
        double tr = R[0][0] + R[1][1] + R[2][2];
        double n4;
        
        if (tr > 0.0f) {
            q[0] = R[1][2] - R[2][1];
            q[1] = R[2][0] - R[0][2];
            q[2] = R[0][1] - R[1][0];
            q[3] = tr + 1.0f;
            n4 = q[3];
        } else if ( (R[0][0] > R[1][1]) && (R[0][0] > R[2][2]) ) {
            q[0] = 1.0f + R[0][0] - R[1][1] - R[2][2];
            q[1] = R[1][0] + R[0][1];
            q[2] = R[2][0] + R[0][2];
            q[3] = R[1][2] - R[2][1];
            n4 = q[0];
        } else if (R[1][1] > R[2][2]) {
            q[0] = R[1][0] + R[0][1];
            q[1] = 1.0f + R[1][1] - R[0][0] - R[2][2];
            q[2] = R[2][1] + R[1][2];
            q[3] = R[2][0] - R[0][2];
            n4 = q[1];
        } else {
            q[0] = R[2][0] + R[0][2];
            q[1] = R[2][1] + R[1][2];
            q[2] = 1.0f + R[2][2] - R[0][0] - R[1][1];
            q[3] = R[0][1] - R[1][0];
            n4 = q[2];
        }
        double scale = 0.5f / double(sqrt(n4));
        
        q[0] *= scale;
        q[1] *= scale;
        q[2] *= scale;
        q[3] *= scale;
    }
    
} //namespace ORB_SLAM
